At parties, Sarah Brown generally hears one of three different responses when she tells people she's an actuary. "You often get, 'Oh, will I have seen you in anything?'" she says, "because they think you're an actress." (In fact she does appear in panto with her local amateur dramatic society, but this is beside the point.)

"Then there's the people who do know exactly what we do, and that can be a bit of a mixed reaction. Some think it's fantastic and go, 'Oh gosh, you must be really clever!' And some people are a bit intimidated, I suppose." She heaves a sigh. "And the other one is where they say, 'A what?' So you say you're an actuary in pensions and explain it, and everyone starts yawning."

Brown and I are facing one another across a table in the Liverpool offices of her employer, Barnett Waddingham. Downstairs, beneath extravagantly high ceilings, uniformed men of a certain age usher visitors politely through the building's marble halls, which evoke the faded clatter of typing pools and umbrella tips. Outside our meeting room sit Brown's smartly dressed colleagues at their partitioned desks, walled around with stacks of immaculately serried files. It is the most orderly office, I think, that I have ever seen. Brown apologises for the messiness of a neat stack of papers that have just been placed on her desk.

So, ahem, just to get things nice and clear, and in case some of our readers may not already know, what is an actuary? "That is the hardest question," she smiles. "I say that we use maths to try to solve business problems. It's all based on probability." So you're a professional guesser? "Don't put that in." She sounds appalled. "It's much more accurate than guessing." More like being a bookie then? "Perfect. Yeah. It is very similar. A bookie takes a bet, and there's a risk that they'll have to pay out a bigger sum later on. Although that's a simpler version, because there's only one variable, whether the horse wins or not."

The kinds of business problems that Brown specialises in concern pension schemes, but other actuaries also deal with things like healthcare and general insurance - working out how much you pay for your car insurance, for instance. "We're trying to work out what [our clients] should pay," she says, "and trying to keep it stable, so they're just paying a sensible amount every year."

Lest you are already stifling a yawn, it may be worth remembering that without actuaries the world economy would collapse in an instant, as nobody would be able to insure anything or plan their investments. Also worth noting is that actuarial work is very difficult. To give you an idea how difficult, and I will only do this once, I have written the following two paragraphs:

You are a company that employs 100 people. You want to start up a final-salary pension scheme for you and them to contribute to. Some of your junior staff will rise through the ranks and be earning top salaries by the time they retire at 65 (by when salaries will be much higher because of inflation, and may also have risen anyway as the country prospers).

Other staff will retire on less money, or may leave the company sooner and drop out of the scheme, or may defer their pension for a few years after they retire. Regrettably, some employees will also die before retirement, and you will need the scheme to be rich enough to provide for their families if this happens. If you were able to fast-forward time and watch all your staff get promoted, leave, die and retire, you would also be able to see the cost of paying their pensions rise, year by year, and work out how much to invest today in order to pay for all the bills as they come up. Unfortunately, you can't do this, so you have a problem. Pay in too much every month and you may ruin the company; pay in too little and you will leave your loyal staff to die in poverty. Now you need an actuary.

"It is complicated," Brown admits, "but you get a lot of help and assistance to do it. And computers the way they are now have powerful spreadsheets to deal with things. But," she sounds a note of caution, "you should always understand what you're doing. That's what annoys me about these big fancy spreadsheets sometimes, that you can sit there and plug the numbers in and it comes out with the answer, but you don't really know what it's been doing behind the scenes. I think it's really important that you do know what is going on behind it all."

Not surprisingly, it takes years of study and experience to learn to understand such things. After achieving 3 As at A-level (in maths, biology and chemistry), Brown studied maths and statistics at Edinburgh University, where she found herself in a common dilemma. "I couldn't decide whether I wanted to be an actuary or an accountant," she explains.

To settle matters, her father, who was the trustee of a pension scheme, managed to find her a work experience placement with the actuaries he used, and another with an accountancy firm. The following summer, Brown reported for duty at the former, and took to it immediately. "The people were the first thing," she recalls. "I just really got on with everybody." She also found that she loved the tasks they gave her, which involved calculating the value of an individual member's pension when it was transferred to another scheme. "To me, it was just doing little puzzles every day," she says, "literally like doing a puzzle book." She was offered a job the following year, and never did try her hand at accountancy.

For four years, Brown worked and studied hard in her new job, passing the 15 exams she needed. "It's not easy to become a qualified actuary," she says proudly. "But that is part of the attraction: not everybody can do it."

She still does puzzles - although she prefers kakuros to sudokus, she explains with a touch of embarrassment, having been hooked like much of the rest of her office as soon they appeared - but after moving to Barnett Waddingham in 2003, her work has taken on rather more importance. Having risen to the role of scheme actuary, though still just 29, she is now personally responsible for all the reports and recommendations that her team of three makes to its clients. This puts her head on the block if something goes wrong, and it also means she has had to learn to communicate well.

"One of the key things I have to do is explain to trustees all the horrendously complex things we're doing in an easy-to-understand way," she says, her eyes lighting up at what is clearly a favourite part of the job. "Often this will mean talking to a factory worker who has no financial knowledge, and they've got to understand what you're going on about, and understand the decisions they're making."

Brown's explanations are not always welcome, however. Rising life expectancies have meant that pensions are becoming more expensive, with the result that she is often the bearer of bad news. "You've just written to a company telling them they've got to pay £200,000 into their pension scheme each year, and they ring, ranting and raving. 'Why are you telling me to do this? There's no way in the world I can afford it! Blah, blah, blah.' And you've got to come to some kind of agreement." This, you sense, is the part of the job she does not like. "We just make recommendations," she protests. "It's up to the company and trustees to agree it. But we tend to get the blame."

The rewards, however, are handsome. In Liverpool, Brown estimates a starting salary for new graduates of £23,000-25,000 a year, rising to the mid-40s after qualification, and to between £50,000 and £60,000 on becoming a scheme actuary. From there it depends on experience, but partners in an actuarial firm can do very well indeed. "Then you're talking three figures definitely," she says.

Compared with other jobs earning similar amounts, the hours are not bad. "It's not too drastic," says Brown. "We tend to be very busy January to April when lots of companies have their year-ends. I tend to get in between 8am and 8.30am, and then go home at 6pm or 6.30pm. And I can always go if I've got something in the evening. There's never been a day when I had to cancel something because I couldn't make it because I was stuck at work."

She stops to think for a moment, considering her lot. "Being an actuary is a really nice job," she says at last, smiling across the table as if this simple point was what she had been getting at all along. "I never once during the day look at my watch to see what time it is."

Curriculum vitae

Current position Associate, Barnett Waddingham, Liverpool

Qualifications BSc in maths and statistics from Edinburgh, Fellow of the Institute of Actuaries

Career low I failed the fellowship exam, which was the last one - although I did get it the next year

Career high Qualifying. You've been working towards this for four years. When the results come out everyone's ringing you and texting you. You just drink champagne for 48 hours, basically